tendsto_right_iff — Mathlib

English

If hlb is a basis for lb, then Tendsto f la lb is equivalent to: for each i, pb i implies f x ∈ sb i eventually for x in la.

Русский

Если hlb — базис lb, то Tendsto f la lb эквивалентно: для каждого i, pb i следует f x ∈ sb i часто в la.

LaTeX

$$$ \mathrm{Tendsto} f\ la lb \iff \forall i,\ pb(i) \to \forall^\infty x in la, f(x) \in sb(i) $$$

Lean4

theorem tendsto_right_iff (hlb : lb.HasBasis pb sb) : Tendsto f la lb ↔ ∀ i, pb i → ∀ᶠ x in la, f x ∈ sb i := by
  simp only [Tendsto, hlb.ge_iff, mem_map', Filter.Eventually]

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